Synchronized switch damping (SSD) is a structural vibration control technique in which a piezoelectric patch attached to or embedded into the structure is connected to or disconnected from the shunt circuit in order to dissipate the vibration energy of the host structure. The switching process is performed by a digital signal processor (DSP) which detects the displacement extrema and generates a command to operate the switch in synchronous with the structure motion. Recently, autonomous SSD techniques have emerged in which the work of DSP is taken up by a low pass filter, thus making the whole system autonomous or self-powered. The control performance of the previous autonomous SSD techniques heavily relied on the electrical quality factor of the shunt circuit which limited their damping performance. Thus in order to reduce the influence of the electrical quality factor on the damping performance, a new autonomous SSD technique is proposed in this paper in which a negative capacitor is used along with the inductor in the shunt circuit. Only a negative capacitor could also be used instead of inductor but it caused saturation of negative capacitor in the absence of an inductor due to high current generated during the switching process. The presence of inductor in the shunt circuit of negative capacitor limits the amount of current supplied by the negative capacitance, thus improving the damping performance. In order to judge the control performance of proposed autonomous SSDNCI, a comparison is made between the autonomous SSDI, autonomous SSDNC and autonomous SSDNCI techniques for the control of an aluminum cantilever beam subjected to both single mode and multimode excitation. A value of negative capacitance slightly greater than the piezoelectric patch capacitance gave the optimum damping results. Experiment results confirmed the effectiveness of the proposed autonomous SSDNCI technique as compared to the previous techniques. Some limitations and drawbacks of the proposed technique are also discussed.